Search engines assist users in locating information found in documents, including, for example, web pages, PDFs, word processing documents, images, other types of files, etc. In order to quickly and effectively search the various documents for relevant information, search engines may index the contents of the documents and use the index to respond to search queries. A search engine for a corpus of documents, for example the Internet, may have a search index including billions of documents. When a search query is received, the search engine processes and executes the query to generate a list of results, or documents responsive to the query. Search queries are often processed using a tree structure, but in a large document corpus, such as the Internet, query processing time may be unacceptably slow using current query processing techniques because users have come to expect minimal time between submitting a request and receiving search results.